Seismograph trace at selected station
This simulation traces seismic rays from an earthquake epicentre through a spherically-symmetric, four-layer Earth model: crust and mantle, lower mantle, liquid outer core, and solid inner core. Body waves bend at boundaries according to Snell's law, sin(θ₁)/v₁ = sin(θ₂)/v₂. Each ray conserves a constant ray parameter p = sin(i)/v, so the path is integrated step by step inward and curves back up at its turning radius.
The epicentre-angle slider rotates the earthquake source around the surface, while the ray-path slider sets how many take-off angles (4–24) are launched. P-waves (orange) penetrate every layer; S-waves (blue, dashed) stop at the outer core because liquids cannot transmit shear. The synthetic seismograph below shows P and S arrival times, illustrating why seismologists use travel-time differences to locate quakes and probe Earth's deep structure.
What is the difference between P-waves and S-waves?
P-waves (primary) are compressional waves that push and pull material along their direction of travel, so they pass through solids and liquids alike. S-waves (secondary) are shear waves that move material sideways and can only travel through solids. P-waves are faster, which is why they always arrive first on a seismogram.
What is the seismic shadow zone?
The shadow zone is the band of epicentral distances, roughly 103° to 142° in this model, where no direct P-waves reach the surface. It exists because the liquid outer core is much slower than the mantle, so rays entering it refract sharply inward. The simulation shades this sector in red around the epicentre.
Why do S-waves stop at the outer core?
S-waves are shear waves and rely on a material's rigidity to propagate. The outer core is liquid iron and nickel, which has no shear strength, so S-waves cannot pass through it. Their absence beyond about 103° was the key historical evidence that Earth's outer core is molten.
The first slider sets the epicentre angle (0°–180°), rotating the earthquake source around the globe and shifting where the shadow zone falls. The second slider sets the number of ray paths launched from the source, between 4 and 24 in steps of two, so you can see a sparse fan or a dense one.
Refraction follows Snell's law, sin(θ₁)/v₁ = sin(θ₂)/v₂. For a spherically-symmetric Earth this becomes the ray-parameter relation p = r·sin(i)/v(r), which stays constant along a ray. A ray turns around where v(r) equals 1/p, and the simulation numerically integrates the angular span as the ray steps inward and back out.
The model uses representative values: about 6.5 km/s for P-waves in the crust, 11.0 km/s in the mantle, 9.0 km/s in the liquid outer core, and 11.3 km/s in the inner core. S-waves in the mantle travel at roughly 64% of the local P-wave speed. These approximate real Earth profiles closely enough to reproduce the shadow zone.
It is a teaching model, not a research tool. It uses piecewise-constant velocities, a simplified four-layer Earth, and an approximate ray integration, so paths and arrival times are illustrative rather than precise. The qualitative physics, however, refraction, the shadow zone, and the S-wave core barrier, matches real seismology well.
Although the outer core deflects rays away from the 103°–142° band, P-waves that pass deep into the core are refracted again and emerge at larger distances. This is why direct P returns past about 142°, just delayed and weakened. The inner core can also reflect and refract energy back toward closer stations.
The lower panel plots a synthetic seismogram for the selected station, marking the P arrival (gold line) and, where the station lies outside the shadow zone, the S arrival (blue line). Arrival times scale with epicentral distance, so the P–S gap widens with distance, the same principle used to estimate how far away a quake occurred.
Networks of seismometers record P and S arrival times from each earthquake, and the differences are inverted to locate the source and image Earth's interior. The very existence of the shadow zone and the missing S-waves revealed the molten outer core, while subtle travel-time variations today map mantle plumes, subducting slabs, and the inner core.